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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
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How to relate toric data and group character?
If I collect the Cartan generators of su(3) or sl(3,C), then the diagonal entries can be arranged as
$$
\begin{pmatrix}
1 &1& -2 \\\
0& 1 &-1
\end{pmatrix}
$$
after a row operation this becomes
$$
…